Describe Data by Range and Interquartile Range

6.DS.3 · Unit 2 · Lesson 5

Name   Period

Objectives / Objetivos

Content Objective: I can find the range and the interquartile range of a data set and use them to describe how spread out the data is.

Language Objective: I can explain what the spread of a data set is using the words range, quartile, interquartile range, and vary.

Key Idea / Idea clave

Measures of Variability: Range & IQR. Formula: Range = Maximum − Minimum | IQR = Q3 − Q1. 1. Range measures the total spread across the entire data set. 2. IQR (Interquartile Range) measures the spread of the middle 50% of data. 3. Both are non-negative distance measures of variability

I Notice / Observo

  • I notice the lowest score in the data set is ___.
  • I notice the highest score in the data set is ___.

I Wonder / Me pregunto

  • I wonder what one number could describe how spread out all the scores are ___.

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Range and Interquartile Range
Rango y rango intercuartílico		Two numbers that describe spread: the range covers all the data, and the interquartile range covers only the middle half.
Dos números que describen la dispersión: el rango cubre todos los datos y el rango intercuartílico solo la mitad central.
Range
Rango		The distance from the least value to the greatest value, found by subtracting: greatest − least.
La distancia del valor menor al mayor, que se halla restando: mayor − menor.
Quartile
Cuartil		One of the three values that cut an ordered data set into four equal-sized groups.
Uno de los tres valores que dividen un conjunto ordenado de datos en cuatro grupos del mismo tamaño.
Interquartile range
Rango intercuartílico		The distance across the middle half of the data, found by subtracting the first quartile from the third: Q3 − Q1.
La distancia a lo largo de la mitad central de los datos: se resta el primer cuartil del tercero: Q3 − Q1.
Variability
Variabilidad		How much the values in a data set differ from one another — whether they sit close together or far apart.
Cuánto se diferencian entre sí los valores de un conjunto de datos: si están juntos o muy separados.
Measure of variation
Medida de variación		A single number that describes the spread of a whole data set. The range and the IQR are both measures of variation.
Un solo número que describe la dispersión de todo un conjunto de datos. El rango y el RIC son medidas de variación.

Practice Preview / Vista previa de práctica

  1. A data set runs from a least value of 12 to a greatest value of 30. What is the range?
    1. 18
    2. 30
    3. 12
    4. 21
  2. A box plot shows: least 68, Q1 75.5, median 83.5, Q3 88, greatest 94. What are the range and the IQR?
    1. Range 26, IQR 12.5
    2. Range 12.5, IQR 26
    3. Range 26, IQR 83.5
    4. Range 20, IQR 12.5
  3. Match each value from the history test data (68, 70, 73, 74, 75, 76, 77, 80, 82, 83, 84, 85, 86, 86, 88, 88, 90, 90, 93, 94) with what it is.
    • 26 → ___
    • 12.5 → ___
    • 83.5 → ___
  4. Find the error
    1. Step 1: Setup — Class A: least 62, Q1 74, median 81, Q3 87, greatest 90.
    2. Step 2: Setup — Class B: least 70, Q1 76, median 81, Q3 84, greatest 90.
    3. Step 3: Step 1 — Both classes have a median of 81.
    4. Step 4: Step 2 — Both classes reached the same greatest score, 90.
    5. Step 5: Step 3 — So the two classes performed the same overall.

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: